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Dynamic factor models with infinite-dimensional factor space: Asymptotic analysis

Mario Forni (), Marc Hallin (), Marco Lippi () and Paolo Zaffaroni

Journal of Econometrics, 2017, vol. 199, issue 1, 74-92

Abstract: Factor models, all particular cases of the Generalized Dynamic Factor Model (GDFM) introduced in Forni et al., (2000), have become extremely popular in the theory and practice of large panels of time series data. The asymptotic properties (consistency and rates) of the corresponding estimators have been studied in Forni et al. (2004). Those estimators, however, rely on Brillinger’s concept of dynamic principal components, and thus involve two-sided filters, which leads to rather poor forecasting performances. No such problem arises with estimators based on standard (static) principal components, which have been dominant in this literature. On the other hand, the consistency of those static estimators requires the assumption that the space spanned by the factors has finite dimension, which severely restricts their generality—prohibiting, for instance, autoregressive factor loadings. This paper derives the asymptotic properties of a semiparametric estimator of the loadings and common shocks based on one-sided filters recently proposed by Forni et al., (2015). Consistency and exact rates of convergence are obtained for this estimator, under a general class of GDFMs that does not require a finite-dimensional factor space. A Monte Carlo experiment and an empirical exercise on US macroeconomic data corroborate those theoretical results and demonstrate the excellent performance of those estimators in out-of-sample forecasting.

Keywords: High-dimensional time series; Generalized dynamic factor models; Vector processes with singular spectral density; One-sided representations of dynamic factor models; Consistency and rates (search for similar items in EconPapers)
JEL-codes: C0 C01 E0 (search for similar items in EconPapers)
Date: 2017
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Related works:
Working Paper: Dynamic Factor Models with Infinite-Dimensional Factor Space. Asymptotic Analysis (2016) Downloads
Working Paper: Dynamic Factor Models with Infinite-Dimensional Factor Space: Asymptotic Analysis (2015) Downloads
Working Paper: Dynamic Factor Models with Infinite-Dimensional Factor Space: Asymptotic Analysis (2015) Downloads
Working Paper: Dynamic Factor Models with In nite-Dimensional Factor Space: Asymptotic Analysis (2015) Downloads
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